<p>给你 3 个正整数&nbsp;<code>zero</code>&nbsp;，<code>one</code>&nbsp;和&nbsp;<code>limit</code>&nbsp;。</p>

<p>一个 <span data-keyword="binary-array">二进制数组</span> <code>arr</code> 如果满足以下条件，那么我们称它是 <strong>稳定的</strong> ：</p>

<ul>
	<li>0 在&nbsp;<code>arr</code>&nbsp;中出现次数 <strong>恰好</strong>&nbsp;为<strong>&nbsp;</strong><code>zero</code>&nbsp;。</li>
	<li>1 在&nbsp;<code>arr</code>&nbsp;中出现次数 <strong>恰好</strong>&nbsp;为&nbsp;<code>one</code>&nbsp;。</li>
	<li><code>arr</code> 中每个长度超过 <code>limit</code>&nbsp;的 <span data-keyword="subarray-nonempty">子数组</span> 都 <strong>同时</strong> 包含 0 和 1 。</li>
</ul>

<p>请你返回 <strong>稳定</strong>&nbsp;二进制数组的 <em>总</em> 数目。</p>

<p>由于答案可能很大，将它对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<b>取余</b>&nbsp;后返回。</p>

<p>&nbsp;</p>

<p><strong class="example">示例 1：</strong></p>

<div class="example-block">
<p><span class="example-io"><b>输入：</b>zero = 1, one = 1, limit = 2</span></p>

<p><span class="example-io"><b>输出：</b>2</span></p>

<p><strong>解释：</strong></p>

<p>两个稳定的二进制数组为&nbsp;<code>[1,0]</code> 和&nbsp;<code>[0,1]</code>&nbsp;，两个数组都有一个 0 和一个 1 ，且没有子数组长度大于 2 。</p>
</div>

<p><strong class="example">示例 2：</strong></p>

<div class="example-block">
<p><strong>输入：</strong><span class="example-io">zero = 1, one = 2, limit = 1</span></p>

<p><span class="example-io"><b>输出：</b>1</span></p>

<p><strong>解释：</strong></p>

<p>唯一稳定的二进制数组是&nbsp;<code>[1,0,1]</code>&nbsp;。</p>

<p>二进制数组&nbsp;<code>[1,1,0]</code> 和&nbsp;<code>[0,1,1]</code>&nbsp;都有长度为 2 且元素全都相同的子数组，所以它们不稳定。</p>
</div>

<p><strong class="example">示例 3：</strong></p>

<div class="example-block">
<p><span class="example-io"><b>输入：</b>zero = 3, one = 3, limit = 2</span></p>

<p><span class="example-io"><b>输出：</b>14</span></p>

<p><strong>解释：</strong></p>

<p>所有稳定的二进制数组包括&nbsp;<code>[0,0,1,0,1,1]</code>&nbsp;，<code>[0,0,1,1,0,1]</code>&nbsp;，<code>[0,1,0,0,1,1]</code>&nbsp;，<code>[0,1,0,1,0,1]</code>&nbsp;，<code>[0,1,0,1,1,0]</code>&nbsp;，<code>[0,1,1,0,0,1]</code>&nbsp;，<code>[0,1,1,0,1,0]</code>&nbsp;，<code>[1,0,0,1,0,1]</code>&nbsp;，<code>[1,0,0,1,1,0]</code>&nbsp;，<code>[1,0,1,0,0,1]</code>&nbsp;，<code>[1,0,1,0,1,0]</code>&nbsp;，<code>[1,0,1,1,0,0]</code>&nbsp;，<code>[1,1,0,0,1,0]</code>&nbsp;和&nbsp;<code>[1,1,0,1,0,0]</code>&nbsp;。</p>
</div>

<p>&nbsp;</p>

<p><strong>提示：</strong></p>

<ul>
	<li><code>1 &lt;= zero, one, limit &lt;= 200</code></li>
</ul>
